Crack growth with non-interpenetration:A simplified proof for the pure Neumann problem

Gianni Dal Maso; Giuliano Lazzaroni

doi:10.3934/dcds.2011.31.1219

Article Contents

2011, Volume 31, Issue 4: 1219-1231. Doi: 10.3934/dcds.2011.31.1219

This issue Previous Article On the regularization of the collision solutions of the one-center problem with weak forces Next Article A variational approach to semilinear elliptic equations with measure data

Crack growth with non-interpenetration: A simplified proof for the pure Neumann problem

Gianni Dal Maso^1, and
Giuliano Lazzaroni^1,

1.
SISSA, via Bonomea 265, 34136 Trieste

Received: December 2009

Revised: December 2010

Published: October 2011

Abstract / Introduction Related Papers Cited by

Abstract

We present a recent existence result concerning the quasistatic evolution of cracks in hyperelastic brittle materials, in the framework of finite elasticity with non-interpenetration. In particular, here we consider the problem where no Dirichlet conditions are imposed, the boundary is traction-free, and the body is subject only to time-dependent volume forces. This allows us to present the main ideas of the proof in a simpler way, avoiding some of the technicalities needed in the general case, studied in [9].

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Mathematics Subject Classification: 35R35, 74R10, 74B20, 49J45, 49Q20, 35A35.

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